Question

A five-letter code is formed by selecting $5$ different letters from the $12$ letters $A,B,C,D,E,F,G,H,I,J,K,$ and $L$ and placing these $5$ letters in the $5$ spaces shown in figure. Calculate the total number of different five-letter codes that are possible.

• A. $\frac{12!}{4!8!}$
• B. $\frac{12!}{(5!)(7!)}$
• C. $\frac{12!}{7!}$
• D. $\frac{12!}{5!}$
• E. $\frac{12!}{4!}$

Answer 1

Answer: (C)

$\frac{12!}{7!}$

In given question total words are $12$ and $A,B,C,D,E,F,G.H,I,J$ and $K$.

In these letters $5$ letters placing in the five spaces to fined code.

Then possible number of code $=$ $\frac{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10\times 11\times 12}{1\times 2\times 3\times 4\times 5\times 6\times 7}=\frac{12!}{7!}$